Thermal conductivity measurement apparatus for one-dimensional material and measurement method

ABSTRACT

A thermal conductivity measurement apparatus for measuring a thermal conductivity of a one-dimensional material includes a substrate, a vacuum chamber receiving the substrate and four spaced electrodes. The one-dimensional material spans across the four spaced electrodes. A middle part of the one-dimensional material, located between the second and third electrodes, is suspended. The present disclosure further provides a method for measuring the thermal conductivity of the one-dimensional material.

This application claims all benefits accruing under 35 U.S.C. §119 fromChina Patent Application No. 200910107401.6 filed on May 8, 2009 in theChina Intellectual Property Office.

BACKGROUND

1. Technical Field

The present disclosure relates to measurement apparatuses andmeasurement methods, and particularly to a thermal conductivitymeasurement apparatus for one-dimensional material and a measurementmethod using the same.

2. Discussion of Related Art

Thermal conductivity is an important parameter which reflects thethermal properties of a material. Selecting a suitable material is animportant issue in heat conduction technology. Therefore, how to exactlymeasure thermal conductivity of a material is important for theapplication of the material.

When the material needed to be measured is a one-dimensionalnanomaterial, such as nanowires or carbon nanotubes, it is moredifficult to measure thermal conductivity. One reason is, that measuringinstruments are large compared to the areas of nanomaterials to bemeasured and so immediately affect the temperature of the material whencontact is made during measurement.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the embodiments can be better understood with referencesto the following drawings. The components in the drawings are notnecessarily drawn to scale, the emphasis instead being placed uponclearly illustrating the principles of the embodiments. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 illustrates a structural schematic view of an embodiment of athermal conductivity measurement apparatus.

FIG. 2 illustrates a curve representing temperature dependence of the Gband frequency value of an object.

FIG. 3 shows a Raman-spectra in a center point O and one of two pointsL₁, L₂ of the suspended part of an object.

DETAILED DESCRIPTION

The disclosure is illustrated by way of example and not by way oflimitation in the figures of the accompanying drawings in which likereferences indicate similar elements. It should be noted that referencesto “an” or “one” embodiment in this disclosure are not necessarily tothe same embodiment, and such references mean at least one.

Referring to FIG. 1, an embodiment of a thermal conductivity measurementapparatus 100 is shown. The thermal conductivity measurement apparatus100 is used to measure a thermal conductivity ω of an object 200. In oneembodiment, the object 200 is a one-dimensional material whosecharacteristic band frequency value of Raman-spectra varies linearlywith its temperature. The one-dimensional material can be aone-dimensional nanometer sized material or one-dimensional micrometersized material. The one-dimensional nanometer material can comprisenanotubes, nanorods, nanowires, nanofibers, nanotips, nanopillars,nanoribbons, and so on.

The thermal conductivity measurement apparatus 100 comprises a supportdevice 10 for supporting the object 200 and a vacuum chamber 20. Thesupport device 10 is located in the vacuum chamber 20. The vacuumchamber 20 can be made of quartz glass. Vacuum degree of the vacuumchamber 20 is approximately 10⁻⁴ Torr.

The support device 10 includes a substrate 30, a first insulated layer34, a second insulated layer 36, a first electrode 342, a secondelectrode 344, a third electrode 362, and a fourth electrode 364.

The substrate 30 defines a groove 302 at a top surface thereof such thata first step 304 and a second step 305 are correspondingly formed at twoflanks of the groove 302. The object 200 is mounted on the first andsecond steps 304, 305 and suspended over the groove 302. The groove 302is located at a center of the substrate 30. The first insulated layer 34is formed on a top surface of the first step 304. The second insulatedlayer 36 is formed on a top surface of the second step 305. The materialof the insulated layers 34, 36 is a dielectric.

The first electrode 342 and the second electrode 344 are mounted on atop surface of the first insulated layer 34 and spaced apart from eachother. The third electrode 362 and the fourth electrode 364 are arrangedon a top surface of the second insulated layer 36 and spaced apart fromeach other. The four electrodes 342, 344, 362, and 364 are parallel toeach other. The four electrodes 342, 344, 362 and 364 can be made ofmolybdenum, platinum, or nickel. In one embodiment, the four electrodes342, 344, 362, and 364 comprises of molybdenum. The first electrode 342and the fourth electrode 364 are connected in series via an ammeter (notshown) and an electrical source (not shown). The second electrode 344and the third electrode 362 are connected via a voltmeter V.

The object 200 spans across and is electrically connected to the fourelectrodes 342, 344, 362, and 364. In detail, a first end of the object200 is mounted on the first electrode 342 and the second electrode 344.A second end of the object 200 is mounted on the third electrode 362 andthe fourth electrode 364. The remaining portion of the object 200located between the second electrode 344 and the third electrode 362 issuspended and can be acted as a suspended part. The object 200 isoriented to be perpendicular to the four electrodes 342, 344, 362, and364. By such arrangement, a current flows into the object 200 throughthe first electrode 342 and flows out the object 200 through the fourthelectrode 364.

Two points where the second electrode 344 and the third electrode 362contact with the object 200 define two opposite ends of the suspendedpart. Constructing a coordinate system for the suspended part, a centerpoint O is the middle point and two points L₁, L₂ are the two oppositeends points of the suspended part.

The thermal conductivity ω of the object 200 can be calculated as:

$\omega = {\frac{P\; \Delta \; L}{S\; \Delta \; T}.}$

Where P is thermal power (heat flow) through the suspended part of theobject 200 along the axial direction thereof; L is a length of thesuspended part of the object 200 which means the distance between thetwo points L₁, L₂; S is an area of the cross section of the object 200;ΔT is a temperature difference between temperatures of the center pointO and one of the two points L₁, L₂.

The thermal conductivity ω of the object 200 is measured by using thethermal conductivity measurement apparatus 100. An example using asingle wall carbon nanotube (SWCNT) as the object 200 is used to explainhow to measure the thermal conductivity ω.

Measurement for L

L is a distance between the second electrode 344 and the third electrode362 of the support device 10. L can be measured by using a scanningelectron electron microscope. When the object 200 is perpendicular withthe four electrodes, the L is equal to the distance between the secondelectrode and the third electrode. L can be measured by using a scanningelectron microscope image of the support device 10 and the scale of theimage. In one embodiment, L is 30 micrometers (μm).

Measurement for S

Shape of the cross section of the object 200 is an annulus. An outerradius R and a wall thickness b of the annulus are measured. The outerradius R of the annulus can be measured by using an atomic forcemicroscope image of the object 200 and the scale of the image. In oneembodiment, the outer radius R of the annulus is 1.8 nanometers (nm).The wall thickness b of the annulus is 0.34 nm and b is a constant forthe object 200. Therefore, S is calculated as S=π(2R−b)b=1.1084π squarenanometers (nm²).

Measurement for P

P relates to total heat which is equal to the summation of heatconvection from the object 200 to ambient air, infrared radiation heat,and heat flowing through suspended part of the object 200 along theaxial direction thereof. When a current I flows through the object 200,the object 200 is heated by the current I and generates the total heat.Due to the high vacuum degree of the vacuum chamber 20, heat convectionfrom the object 200 to ambient air may be neglected. The infraredradiation heat is also a very small portion of the total heat and canalso be neglected. Therefore, when the object 200 is heated by thecurrent I, the total heat is taken to equal the heat flowing through theobject 200 along an axial direction of the object 200. The total thermalpower is equal to the total heat divided by time. The thermal power P isequal to the heat flowing through the object 200 along an axialdirection of the object 200 divided by time. Therefore, the totalthermal power is equal to the thermal power P flowing through the object200 along an axial direction of the object 200. The total thermal powerP_(total) can be calculated as P_(total)=UI; therefore, the thermalpower P flowing through the object 200 is equal to P_(total) and canalso be calculated as P=UI. U is amount of voltage across the suspendedpart of the object 200, and I represents the current flowing through theobject 200.

An embodiment for obtaining U and I includes the following steps:

(A) placing the object 200 on the surfaces of the four electrodes 342,344, 362, and 364 of the support device 10;

(B) placing the object 200 and the support device 10 in the vacuumchamber 20;

(C) applying I through the object 200, and the object 200 is heated bythe current and reaches heat balance; the heat steadily conducts fromthe center point O to the two ends L₁, L₂ of the object 200, because thetemperature at the center point O of the suspended object 220 is higherthan that of the two points L₁, L₂ which are contacted with thesubstrate 30;

(D) reading the ammeter and obtaining the value of I; for the testedSWCNT, I is 0.298 microampere(μA); and

(E) reading the voltmeter and obtaining the value of U; for the testedSWCNT, U is 1.175 volts(V).

Therefore, P=UI=3.5×10⁻⁷ Watts (W).

In one embodiment, step (A) includes the following steps:

Step A1, providing a growing substrate on a lateral side of the firstelectrode 342 or the fourth electrode 362 and placing the growingsubstrate and the support device 10 in a growing chamber.

Step A2, providing a ferric trichloride solution of concentration about10⁻⁶-10 ⁻⁵ mol/L. In one embodiment, the ferric trichloride solution ofconcentration is 3×10⁻⁶ mol/L. The ferric trichloride solution works asthe catalyst precursor. The concentration of the ferric trichloridesolution is low enough to ensure an individual SWCNT is formed on thesurfaces of the growing surface.

Step A3, heating up the ferric trichloride solution to 950° C. andflowing mixed gas comprising H₂ and He into the growing chamber at arate of 60-200 cubic centimeter per minute(cm³/min.);

Step A4, adding carbon source gas into the growing chamber as the carbonsource gas and growing an individual SWCNT on the surfaces of thegrowing surface. In one embodiment, the carbon source gas is H₂ and CH₄.When an individual SWCNT is grown, the SWCNT falls on the surfaces ofthe four electrodes 342, 344, 362, and 364 by controlling the directionof the carbon source gas. The grown SWCNT has no support so that itfalls down across the surfaces of the four electrodes easily andperpendicular with the four electrodes by the force of the flowingcarbon source gas.

The SWCNT is not need to be grown in vacuum. Alternatively, anindividual SWCNT can be placed on the surfaces of the four electrodes342, 344, 362 and 364 of the support device 10 directly.

Measurement for ΔT

ΔT is obtained by using a characteristic band frequency value differenceΔC between the center point O and one of the two points L₁, L₂ and aslope K of a curve representing the temperature dependence of thecharacteristic band frequency value of Raman-spectra of the object 200.ΔT can be calculated as: ΔT=KΔC. The characteristic band frequency valueof the Raman-spectra is different when the object 200 is made ofdifferent material. For a SWCNT, the characteristic band frequency valueof Raman-spectra is G band frequency. ΔG is the G band frequency valuedifference between the center point O and one of the two points L₁, L₂of the suspended part of the object 200. The G band is the highest bandin the Raman-spectra.

An embodiment for obtaining ΔT includes the following steps:

Step 21, obtaining a plurality of the G band frequency values ofRaman-spectra of the object 200 at different predetermined temperaturesafter mounting the object 200 on the four electrodes 342, 344, 362, and364 but before the current flows into the one-dimensional material andgetting a plurality of data corresponding to the different predeterminedtemperatures.

The support device 10 may be placed in a temperature controllingapparatus. The temperature of the support device 10 and the object 200can be controlled by the temperature controlling apparatus. The object200 is placed in the support device 10 and has no electricity flowingthrough it. The temperature of the temperature controlling apparatus canbe predetermined. The G band frequency value of Raman-spectra of theobject 200 is measured at the predetermined temperature of thetemperature controlling apparatus.

Step 22, fitting the plurality of data to a curve representing thetemperature dependence of the G band frequency value of Raman-spectra.The method for fitting a plurality of data can be with the use of linearregression, non-linear regression, or with a spline function. In oneembodiment, the data is fit by linear regression and a broken line isobtained as shown in FIG. 2. The broken line is the curve representingthe temperature dependence of the G band frequency value ofRaman-spectra of the object 200.

Step 23, calculating a slope K of the curve representing the temperaturedependence of the G band frequency value of Raman-spectra. In oneembodiment, referring to FIG. 2, the slope K of the broken line is−0.0257 cm⁻¹/K.

Step 24, comparing the G band frequency value of Raman-spectra at thecenter point O to the G band frequency value of Raman-spectra of one ofthe two points L₁, L₂ to obtain ΔG. The G band frequency value ofRaman-spectra at the center point O of the object 200 is defined as G₁.The G band frequency value of Raman-spectra of one of the two points L₁,L₂ is defined as G₂.

G₁ and G₂ are measured by a Roman spectrometer. A Raman-laser emitted bythe Roman spectrometer is focused at the center point O and one of thetwo points L₁, L₂ of the object 200 to obtain two Raman-spectrasthereof. Because the resolution ability of the Raman-laser can reach to1 μm so that each point of suspended part of the object 200 having alength of 30-micrometrer can be accurately measured. The wavelength ofthe Raman-laser employed is 514.5 nm. When a current I flows through theobject 200, the object 200 is heated by the current and reaches heatbalance. After reaching heat balance, there is a steady temperaturedistribution along the object 200 and G₁ and G₂ of the object 200 can bemeasured subsequently. The number of the measurement times that thecenter point O and one of the two points L₁, L₂ of the object 200 aremeasured can exceed three times. A final result is an average of themeasuring results.

Referring to FIG. 3, G₁ is 1567.6 centimeters⁻¹(cm⁻¹), G₂ is 1577.7cm⁻¹. Therefore, ΔG=G₁−G₂=1567.6 cm⁻¹−1577.7 cm⁻¹=−10.1 cm⁻¹.

Step 25, substitute the value of the ΔG and K into the formula ΔT=KΔG.Thus, ΔT is calculated as ΔT=(−10.1 cm⁻¹)(−0.0257 cm⁻¹/K)=393K.

At last, for SWCNT,

$\omega = {\frac{P\; \Delta \; L}{S\; \Delta \; T} = {\frac{U\; I\; \Delta \; L}{{\pi ( {{2R} - b} )}b\; \Delta \; G\; K}.}}$

Where P=UI=3.5×10⁻⁷ W, L=30 μm, S=π(2R−b)b=1.10842π and ΔT=393K. Then,

ω≈2400 W/mK

Therefore, the thermal conductivity ω of SWCNT is 2400 W/mK.

In conclusion, the present disclosure relates to a non-contactmeasurement apparatus and measurement method so as to avoid the object200 contact with elements whose heat capacity is large. Therefore, thetemperature of the object 200 is steady and the result of themeasurement is more exact.

Depending on the embodiments, certain of the steps described may beremoved, others may be added, and the sequence of steps may be altered.It is also to be understood that the description and the claims drawn toa method may include some indication in reference to certain steps.However, the indication used is only to be viewed for identificationpurposes and not as a suggestion as to an order for the steps.

It is to be understood, however, that even though numerouscharacteristics and advantages of the present embodiments have been setforth in the foregoing description, together with details of thestructures and functions of the embodiments, the disclosure isillustrative only, and changes may be made in detail, especially inmatters of shape, size, and arrangement of parts within the principlesof the disclosure.

1. A thermal conductivity measurement apparatus for measuring a thermalconductivity of a one-dimensional material, the thermal conductivitymeasurement apparatus comprising: a substrate; a vacuum chamberreceiving the substrate; a groove is defined in the substrate such thata first step and a second step are located at two flanks of the groove;and four spaced electrodes comprising first, second, third and fourthelectrodes spaced apart from each other, the first and second electrodesare located on the first step, the third and fourth electrodes arelocated on the second step; and the four electrodes are capable ofsupporting a one-dimensional material so that the one-dimensionalmaterial is suspended above the groove.
 2. The thermal conductivitymeasurement apparatus of claim 1, further comprising: a first insulatedlayer located on the first step; a second insulated layer located on thesecond step; and the first electrode and the second electrode arelocated on the first insulated layer, and the third electrode and thefourth electrode are mounted on the second insulated layer.
 3. Thethermal conductivity measurement apparatus of claim 1, wherein thefirst, second, third and fourth electrodes are parallel to each other.4. The thermal conductivity measurement apparatus of claim 1, whereinthe groove is located at a center of the substrate.
 5. The thermalconductivity measurement apparatus of claim 1, wherein the fourelectrodes are electrically connected to the one-dimensional material,the first electrode and the fourth electrode are coupled to an ammeterand an electrical source, the second electrode and the third electrodeare in parallel with a voltmeter.
 6. A method for measuring a thermalconductivity of a one-dimensional material, the method comprising:providing the one-dimensional material whose characteristic bandfrequency value of Raman-spectra varies linearly with its temperatureand a thermal conductivity measurement apparatus; wherein the thermalconductivity measurement apparatus comprises: a substrate and fourelectrodes comprising first, second, third and fourth electrodes spacedapart from each other, a middle part of the one-dimensional materiallocated between the second and third electrodes and being suspended toact as a suspended part; obtaining a length L of the suspended part ofthe one-dimensional material and a cross sectional area S of theone-dimensional material; connecting the four electrodes with theone-dimensional material; heating the one-dimensional material with acurrent and the one-dimensional material reaches heat balance; acquiringa power P flowing through the suspended part of the one-dimensionalmaterial along the axial direction; obtaining a temperature differenceΔT between a middle point and one of the two end points of the suspendedpart of the one-dimensional material; and calculating the thermalconductivity ω of the one-dimensional material in accordance with:$\omega = \frac{P\; \Delta \; L}{S\; \Delta \; T}$
 7. The methodof claim 6, wherein the thermal power P is calculated according to P=UI;U is the value of the voltage of the suspended part of theone-dimensional material, and I is the value of the current flowingthrough the one-dimensional material.
 8. The method of claim 6, whereinobtaining the temperature difference ΔT comprises the following steps:acquiring a plurality of the characteristic band frequency values ofRaman-spectra of the one-dimensional material at different predeterminedtemperatures and getting data corresponding to the differentpredetermined temperatures; fitting the data to obtain a linerepresenting the temperature dependence of the characteristic bandfrequency value of Raman-spectra; calculating a slope K of the line;comparing the characteristic band frequency value of Raman-spectra inthe middle point O to the characteristic band frequency value ofRaman-spectra of one of the two end points L₁, L₂ to obtain thecharacteristic band frequency value difference ΔC between the middlepoint and one of the two end points of the suspended part of theone-dimensional material; and determining the value of ΔT according tothe formula ΔT=KΔC.
 9. The method of claim 8, wherein theone-dimensional material is an individual single wall carbon nanotubeand characteristic band frequency value for the single wall carbonnanotube is G band frequency value, and obtaining the temperaturedifference ΔT comprises the following steps: obtaining a plurality ofthe G band frequency values of Raman-spectra of the single wall carbonnanotube at different predetermined temperatures after mounting thesingle wall carbon nanotube on the four electrodes but before thecurrent flows into the one-dimensional material and getting a pluralityof data corresponding to the different predetermined temperatures;fitting the plurality of the data to obtain a line representing thetemperature dependence of the G band frequency value of Raman-spectra;calculating a slope K of the line; comparing the G band frequency valueof Raman-spectra in the middle point O to the G band frequency value ofRaman-spectra of one of the two end points L₁, L₂ to obtain the G bandfrequency value difference ΔG between the middle point and one of thetwo end points of the suspended part of the single wall carbon nanotube;determining the value of the ΔT according to the formula ΔT=KΔG.
 10. Themethod of claim 9, wherein the G band frequency values of the middlepoint and one of the two end points of the suspended part are measuredby focusing a Roman-laser at the middle point and one of two end pointsof the suspended part of the single wall carbon nanotube.
 11. The methodof claim 9, wherein the middle point and one of the two end points ofthe suspended part are measured more than three times.
 12. The method ofclaim 9, wherein fitting the plurality of data comprises the use oflinear regression, non-linear regression or with a spline function. 13.The method of claim 9, wherein the thermal conductivity of the singlewall carbon nanotube is calculated in accordance with:$\omega = {\frac{P\; \Delta \; L}{S\; \Delta \; T} = \frac{U\; I\; \Delta \; L}{{\pi ( {{2R} - b} )}b\; \Delta \; G\; K}}$wherein P=UI=3.5×10⁻⁷ W, L=30 μm, S=π(2R−b)b=1.1084π, ΔT=393K and ω≈2400W/mK.